John the Ripper is a free and open source password cracker that can help you detect weak passwords. It's distributed primarily in source code form, but native "pro" versions are available for both Linux and Macs as well; the prepackaged Linux version is priced starting at $39.95. Another similar tool, incidentally, is THC Hydra.
Short for "Network Mapper," Nmap is a free and open source utility for network exploration or security auditing, but it can also be useful for network inventory, managing service upgrade schedules, and monitoring host or service uptime. Nmap runs on all major computer operating systems. Oddly, it has even been featured in movies including The Matrix Reloaded, The Bourne Ultimatum and The Girl with the Dragon Tattoo.
Chkrootkit is a free tool designed to check locally for signs of a rootkit infection on your Linux machine. The free software is a very popular choice, but Rootkit Hunter is another, like-minded alternative.
With more than five million downloads to date, Nessus is one of the most popular vulnerability scanners in the world, its makers say. The proprietary software features high-speed discovery, configuration auditing, asset profiling, sensitive data discovery and vulnerability analysis of your security posture. Personal use of Nessus is free, but enterprises must purchase a subscription costing $1,200 per year per Nessus scanner.
There are, of course, countless other security tools for Linux out there, many of them excellent as well. What are your favorites?